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- W3088797660 abstract "We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M in mathbb{Q}^{d times d}$, an initial vector $xinmathbb{Q}^{d}$, a granularity $gin mathbb{Q}_+$ and a rounding operation $[cdot]$ projecting a vector of $mathbb{Q}^{d}$ onto another vector whose every entry is a multiple of $g$, we are interested in the behaviour of the orbit $mathcal{O}={ }$, i.e., the trajectory of a linear dynamical system in which the state is rounded after each step. For arbitrary rounding functions with bounded effect, we show that the complexity of deciding point-to-point reachability---whether a given target $y inmathbb{Q}^{d}$ belongs to $mathcal{O}$---is PSPACE-complete for hyperbolic systems (when no eigenvalue of $M$ has modulus one). We also establish decidability without any restrictions on eigenvalues for several natural classes of rounding functions." @default.
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- W3088797660 date "2020-12-15" @default.
- W3088797660 modified "2023-10-15" @default.
- W3088797660 title "Reachability in Dynamical Systems with Rounding" @default.
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- W3088797660 doi "https://doi.org/10.4230/lipics.fsttcs.2020.52" @default.
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